Question
The tangent at P on the ellipse meets the minor axis in Q, and PR is drawn perpendicular to the minor axis and C is the centre. Then CQ . CR =
- b2
- 2b2
- a2
- 2a2
Hint:
assume the coordinates of the point P and find out the coordinates of the points Q and R in terms of the point P. find the lengths of the line segments and find the answer.
The correct answer is: b2
b2
Let the point p be (t,u)
The equation of tangent at p : xt/a2+yu/b2=1
Coordinates of point Q : (0, b2/u)
Equation of perpendicular drawn at P to the minor axis:
y= u
coordinates of R: (0,u)
length of CQ = b2/u
length of CR = u
hence, CQ.CR =
the y coordinate of line parallel to the x axis can be calculated from the equation of the line.
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